Developing a Growth Mindset for Math - nctm.confex.com · mean) theories of intelligence. Implicit...

Developing a Growth Mindset for Math

Supporting Productive Failure

David Dockterman, Ed.D.Harvard Graduation School of EducationScholastic Education

1Friday, April 19, 13

Dockterman, NCSM/NCTM 2013

Make it “relevant”Make it “fun”

Historical tendency: “You know how kids love...”

• video games

• computers

• television

• radio

• movies

• magic lanterns



What motivates humans, including students?

Center on Education Policy

1. Competence (progress)

2. Control/Autonomy (agency)

3. Interest/Value (purpose)

4. Relatedness (community/status)

http://www.cep-dc.org





1. Competence AND Confidence

• Perceived ability matters more than actual ability

• Girls often do better in math/science than boys but feel less capable

• Fixed vs Growth Mindset


Dockterman, NCSM/NCTM 2013Dockterman, NCSM/NCTM 2013

– Carol Dweck, Ph. D. Author of MindSet



considered artifacts of high prior ability or achieve-ment (cf. Pomerantz & Saxon, 2001). However, asstudents made the transition to junior high school,their theory of intelligence became a significantpredictor of their mathematics achievement (rs ran-ged from .12 in the fall term of seventh grade, po.05,to .20 in the spring term of eighth grade, po.05).Moreover, an incremental theory of intelligence atthe beginning of junior high school predicted highermathematics grades earned at the end of the secondyear of junior high school (b5 .17, t5 3.40, po.05),controlling for the effect of math achievement testscores before entering junior high school (b5 .43,t5 8.48, po.05). This result held (b5 .10, t5 2.50,po.05) using math grades earned in the first term ofjunior high school (b5 .70, t5 17.50, po.05) insteadof end of sixth-grade test scores.

Relation of Theory of Intelligence to Mathematics GradeGrowth Trajectories

To assess the contribution of theory of intelligenceto the trajectory of achievement over the junior highschool transition, we looked at the growth curves inmathematics grades for students with different im-plicit theories. Growth curves were computed usingBryk and Raudenbush’s (1987, 1992) HierarchicalLinear Modeling (HLM) program. The Level 1equation was

Yit ! b0i " b1i#time$ " eit;

where b0 represents the intercept, or the averagemath grades at Time 1 (i.e., time was coded as 0, 1, 2,3), and b1 is the slope, or average change per unit oftime. The trajectory of math grades was computedacross the four assessments (fall seventh grade,spring seventh grade, fall eighth grade, and springeighth grade).

Implicit theory of intelligence was entered at Lev-el 2. Before computing the growth curves, wewanted to control for potential differences betweenthe four cohorts. Although all students within eachcohort had the same teacher and curriculum, not allcohorts had the same teacher; thus, there could bedifferences in the grading practices or efficacy ofteachers between cohorts. Therefore, dummy vari-ables were created for each cohort and entered intothe equation at Level 2. The Level 2 equation for thegrowth curves was

b0i ! g00 " b01#theory$ " g02#Cohort 1$" g03#Cohort 2$ " g04#Cohort 3$

b1i ! g10 " g11#theory$ " g12#Cohort 1$" g13#Cohort 2$ " g14#Cohort 3$:

By entering the cohort dummies into the Level 2equations, we are estimating the mean-level growthadjusted for possible cohort differences. The averagegrade at Time 1 for the sample was 72.05, about aC% . There was no main effect of theory of intelli-gence on Time 1 grades (b5 .98, t5 1.47, ns) and nochange in average grade across the 2 years (b5 .39,t5 .90, ns). However, there was a significant effect oftheory of intelligence on change in grades (b5 .53,t5 2.93, po.05). The significant effect of theory ofintelligence at Level 2 represents an interaction be-tween theory of intelligence and time. This inter-action suggests that the math achievement growthpatterns differ based on one’s theory of intelligence.To understand this interaction, we followed theguidelines suggested by Aiken and West (1991)and graphed the interaction using scores of 1 SDabove and below the theory of intelligence mean (seeFigure 1).

Although students with the entity and incremen-tal theories did not differ significantly in their mathachievement test scores as they entered junior highschool, as these results show, they began to pull apartover the 2 years of junior high school. We found thattheory of intelligence is related to a set of motiv-ational constructs; thus, we need to take the motiv-ational constructs into account when discussing theeffect of theory of intelligence. In the next section, weaddress the role of these motivational constructs.

Mediational Pathways

One goal of the present study was to go beyonddocumenting the relation between theory of intelli-gence and academic achievement to explain why thisrelation exists. However, we had four mediators thatmight, individually or in combination, explain this

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Fall 7th Grade Spring 7th Grade Fall 8th Grade Spring 8th Grade

Mat

h G

rade

s

Incremental

Entity

Figure 1. Graph of interaction effect of theory of intelligence andtime on math achievement: Growth curves of predicted mathe-matics grades over 2 years of junior high school for students withincremental (11 SD above the mean) and entity (% 1 SD below themean) theories of intelligence.

Implicit Theories and Achievement 251

Growth Mindset ResultsBlackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit

Theories of Intelligence Predict Achievement Across an Adolescent Transition : A Longitudinal Study and an Intervention. Child Development, 78(1), 246–263. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8624.2007.00995.x/full


http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8624.2007.00995.x/full





What’s Your Fixed Mindset? Are you a video game player?



Fixed vs Growth Mindset

Fixed Mindset

• “I’m not...”

• avoid failure

• mistake = can’t do (I’m not)

Growth Mindset

• “I can if...”

• look for challenges

• mistake = learning opportunity



Shift relationship with failure

• “struggle” and “mistakes” are not typically rewarded in school

• In games, failure is the norm. Success is the exception.

• In school, for struggling students, mistakes = “I’m stupid.”

• In good games, mistakes = “I need to try again.” “What can I do differently?”



Give Students a Running Start

• we persevere when we believe we can succeed

• but we need evidence

• shaky confidence + early failure = total shutdown

• games provide a gradual slope

Slice It! -- com2us.com



But move quickly to the edge

The Math Curriculum

edge of competence

Know & Do

“I’m good!”

Just the Right Frustration Can be Very Satisfying

“I can’t”“I’m bored”

Zone of Proximal Development



Shift the Reference Point

• Set the expectation for struggle

• When low SES or minority students struggle at college...

• don’t belong, drop out

• but if expect to struggle, then more likely to stay and graduate



• with words

• by modeling with your own mistakes

• using examples

• by teaching about growth mindset

“Wow, that problem didn’t turn out the way I

wanted. Let me see if I can figure out what I did wrong....Ah, maybe that’s it.

Good. I learned something new. That was a good

Words, Models, & Knowledge vs

“Let’s start with an

easy one.”

“This might take a

few tries.”



› DAY 1

PROFILE NUMBER

Some people believe that you are born with or without certain skills. Others believe that you can become better at anything through hard work and effort. Let's find out what you think.

Week 1FIRSTTWO WEEKS

› Add up all the profi le numbers and write the total.

Agree Disagree

A No matter how much intelligence you have, you can always change it a good deal. 6 5 4 3 2 1

B I like my work best when it makes me think hard. 6 5 4 3 2 1

C I like work that I'll learn from even if I make a lot of mistakes. 6 5 4 3 2 1

D When something is hard, it just makes me want to work more on it, not less. 6 5 4 3 2 1

E You can learn new things, but you cannot really change your basic level of intelligence. 1 2 3 4 5 6

F I like my work best when I can do it really well without too much trouble. 1 2 3 4 5 6

G I like my work best when I can do it perfectly without any mistakes. 1 2 3 4 5 6

H To tell the truth, when I work hard, it makes me feel as though I'm not very smart. 1 2 3 4 5 6

TOTAL

Mindset Scan

Decide how much you agree or disagree with each statement. Circle and write your answer.

RANKING GUIDEAgreea lot

Agree Agree a little

Disagree a little

Disagree Disagree a lot

6 5 4 3 2 1

THIS IS NOTA TEST!

It is an opinion survey about your beliefs,goals, and

thoughts on intelligence.

5A MATH 180

What’s Your Mindset?

• http://www.mindsetworks.com


http://www.mindsetworks.com

http://www.mindsetworks.com


Use Appropriate Feedback

• Can’t learn from failure without feedback

• Reinforce the right

• Correct the wrong

• Imagine practicing putting without seeing if the ball goes in the hole



Corrective Feedback

• or practicing free throws without seeing if the ball goes in the basket



Corrective Feedback

• or practicing math procedures without knowing if the answers are correct

• digital games provide immediate feedback and can be incredibly failure tolerant

• so do simulations and visual models

• try...see results...revise...repeat

• provides a sense of control



Show Progress

• Progress -- Harvard Business Review #1 big idea for 2010

• Marketers motivating us

• Motivating ourselves

• Making long waits a little more tolerable



Progress through Levels How far to go

Angry Birds -- rovio.com



Progress through Skills FASTT Math Next Generation

FASTT Math -- scholastic.com/fasttmath



Student Dashboards MATH 180



2. Control/Autonomy

• Our brains may not be rational, but they do rationalize

• “If you make me do it, I must not want to do it”

• Intrinsic motivation fueled by choice, undermined by outside control

• But we don’t want to give the choice not to participate



Choices

• Personalized space

• How to get there

• Strategies

• Choice Architecture



Manage the Stakes

frontier learning routine performance

failure tolerant goal of error-free

low stakes high stakes



Learning




Instruction



Practicing




Practice

formative assessment

learning tasks



Performing




Performance Assessment



Give students some control over readiness...




Practice

lots of replay

improve speed & accuracy



3. Interest/Value (Purpose)

• “When will I ever use this?”

• Short-term value: Is this relevant? OR Is it just interesting?

• Long-term value: “I need this for college.” “I need this for...”

• It doesn’t work to TELL students that it’s important for them.



Which Number Doesn’t Belong?

9 16 25 43



Purpose Situating math in real stories

Start with Applicationhttp://www.scholastic/math180


http://www.scholastic/math180

http://www.scholastic/math180


4. Relatedness/Community

• The quest for status may be our most basic evolutionary drive.

• Risky fish get the girls.

• Humans crave social acceptance, and self-efficacy (and grades) are related to peer group support.

• Build a growth mindset classroom culture



Mastery vs Performance

Mastery

• Personal progress -- where am I vs where I was before

• all about getting better

• best for struggling students who have a history of failure

• choose when and with whom to share growth

Performance

• Competitive -- where am I compared to others

• all about winning

• good for high performers who think they have a chance of winning

• performance always on display



Who Cares?

• Teacher - Student

• Parent - Student

• Student - Student



The power of YET (Carol Dweck)

• “You haven’t mastered those skills...yet.”

• “You’re not explaining the connection between the graph and the equation clearly...yet.”

• “We haven’t reached all the students...yet”



“If you think you can catchthe bus, you will run for it.” - Lee Peng Yee



Questions or [email protected]


mailto:[email protected]

mailto:[email protected]

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